RMS, Peak and Average Value Formulas

RMS, peak, peak-to-peak and average value formulas for sine, square and triangle waves, form factor and crest factor, with a worked example and table.

The formulas for a sine wave

The average of a full sine cycle is zero, so the average value quoted is that of the rectified wave, over a half cycle. The same relations hold for current. RMS is the value that gives the same heating in a resistor as a direct voltage of that size.

Worked example: a 230 V supply

1. Vpeak = 1.4142 × 230 = 325.3 V
2. Vpp = 2 × 325.3 = 650.5 V
3. Vavg = 2 × 325.3 / π = 207.1 V (half-cycle average)

Other waveforms with a 100 V peak

Frequently asked questions

Why is the supply quoted as an RMS value?

The RMS value produces the same heating in a resistor as the same direct voltage, so 230 V AC heats a heater like 230 V DC.

Do all meters read RMS?

No. Many cheap meters measure the average and scale it for a sine wave. They read wrongly on distorted waveforms. A true-RMS meter does not have this fault.

What is the crest factor used for?

It is the peak divided by the RMS value. A high crest factor means high peaks, which matters for the range of meters and the sizing of drives and UPS inverters.

Are these formulas valid for a distorted wave?

The ratios above are for the ideal shapes. For a distorted wave, measure the RMS or compute it from the harmonics.

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